%I
%S 7,11,13,2,4,8,14,1,11,13,2,8,14,1,7,11,2,14,1,7,11,13,2,8,11,13,2,14,
%T 7,11,2,8,11,2,14,11,2,8,13,2,11,2,2,14,11,2,8,13,13,2,14,2,8,13,11,2,
%U 14,13,13,2,14,2,2,13,13,13,2,14,2,2,13,14
%N A Matrix Markov based on solved permutation Matrices Modulo 15 as 8 X 8 matrices extracted from the primes relative to the first set of eight primes free of {3,5}.
%C This method was a difficult model to program: it bifurcated at higher iterations to gives mostly {2,13,14} leaving out the other values. Observationally in terms of the modulo 10 endings {1,3,7,9} the modulo 15 ending pair as: 1 > {1,11},3 > {8,13},7 > {2,7},9 > {4,14} The idea is that an elliptically polarized partitioning of the primes should behave as permutation of these eight modulo 15 endings.
%F v[n]=vector v[n1] permutated by Matrix M[n] a(n+m1) =v[n][[m]]
%t (*a> Prime[4]to Prime[12 modulo 15 as the reference sequence*) a = {7, 11, 13, 2, 4, 8, 14, 1}; (* finds permutations of the reference sequence to match the actual primes*) M = Table[Table[If[Mod[Prime[i + n], 15]  a[[m]] == 0, 1, 0], {n, 1, 8}, {m, 1, 8}], {i, 4, 68, 8}]; (* matrix Markov switches the permutation matrics in order*) v[0] = a; v[n_] := v[n] = M[[1 + Mod[n, 8]]].v[n  1] a0 = Flatten[Table[v[n][[m]], {n, 0, 8}, {m, 1, 8}]]
%K nonn,uned
%O 0,1
%A _Roger L. Bagula_, Apr 06 2006
